Strýcová, the world number 33, came from a set down to beat the 52nd-ranked, 19-year-old Kenin 6-7 (5/7), 6-1, 6-4 in two hours and 43 minutes.
Siniaková, the world number 31, then saw off 63rd-ranked Riske 6-3, 7-6 (7/2).
The hosts are a win away from their sixth title in the last eight editions and their 11th overall, including five as the former Czechoslovakia. The United States have lifted the trophy a record 18 times.
The 32-year-old Strýcová, who has announced her retirement from Fed Cup duty after the final, struggled with her serve throughout a nervous first set.
Strýcová and Fed Cup debutant Kenin earned two breaks each, with the more aggressive US teenager taking the set in a tie-break.
But, propelled by the sold-out O2 Arena with 14,500 fans, the four-time Fed Cup winner regained composure in the second to sweep aside the Russia-born Kenin, who is still in search of her maiden WTA singles title.
Strýcová took a 5-2 lead in the third and despite giving up two breaks, she took the set 6-4.
“For me, it was a lot of emotions,” Strýcová said on court after the win.
“I fought every ball and I’m so happy that I could win today in front of such a crowd. It means a lot to me.”
“Every point is very important and I’m very happy I could do it today.”
Kenin admitted she was “a little bit overwhelmed” by her debut.
“I was pretty nervous but I was able to handle it,” she said.
“In the second set I got a lot of break opportunities, but she just played too good. so credit to her.”
Siniaková cruised through the first set of her encounter with Riske, forging ahead through a pair of breaks after indulging in groundstrokes and long rallies.
Riske went 3-1 up in the second set, but Siniaková levelled and took the set to a tie-break which she dominated to seal victory.
“I was just trying to focus on every point (in the tiebreak),” said Siniaková.
“Actually, after the first point I was thinking, you know, you’ve played so many tiebreaks this year and you won almost all.”
“It couldn’t be better, but it isn’t finished yet so we need to be ready for tomorrow.”
The US are missing Sloane Stephens, Serena Williams, Venus Williams, and Madison Keys, while the Czechs are without Karolína Plíšková and two-time Wimbledon champion Petra Kvitová.
On Sunday, Siniaková is due to face Kenin and Strýcová will then take on Riske.
Siniaková and Barbora Krejčíková are then scheduled to face Danielle Collins and the Czech Republic-born Nicole Melichar in the final doubles rubber.
But the teams may change and if Kvitová gets better, she might appear on the court.
“We need to discuss that. It will definitely be easier to put the team together when we’re 2-0 up,” said Czech captain Petr Pála.